Using factor theorem, factorize each of the following polynomials : `x^3+2x^2-x-2`

Explanation

`p(x)=x^3+2x^2-x-2`
Factors of `-2` are` ±1,±2`.
`p(1)=1+2-1-2=0`
By trial and error, `1` is a zero of `p(x)`.
So by factor theorem, `x-1` is a factor of `p(x)`.
`p(x)=x^3+2x^2-x-2`
` =x^3-x^2+3x^2-3x+2x-2`
` =x^2(x-1)+3x(x-1)+2(x-1)`
`=(x^2+3x+2)(x-1)`
` =(x^2+2x+x+2)(x-1)`
` =[x(x+2)+1(x+2)](x-1)`
` =(x+1)(x+2)(x-1)`